In order to achieve this, we strengthen our interpretation for a set of desirable option sets \(K_{}\) .
That is, for any \(A_{}\in {Q}\) , \(A_{}\in K_{}\)  is henceforth taken to mean that there is at least one gamble \(f\)  in \(A_{}\)  that is strictly desirable [1]}, [2]},There may arise, due to Walley's [1]}, [2]} perhaps unfortunate introduction of this terminology, some confusion in the reader's mind about the use of `strict'. In most accounts of preference relations, the term `strict preference' refers to `(weak) preference without indifference', and it is also in this sense that we have used the term `strict preference' in the Introduction. Walley uses the moniker `strict' for a stronger requirement, which is essentially based on some lower (or linear) prevision being strictly positive. We maintain this rather unhappy use of terminology here merely for historical reasons, but insist on warning the reader about the possible confusion this may entail. in the sense that there is some \(\epsilon \in \mathbb {R}_{>0}\)  such that \(f-\epsilon \)  is desirable, where—as before for \(\mu \) —we identify the real number \(\epsilon \)  with the constant gamble that takes the value \(\epsilon \) .
